Damage induced stress-softening in the torsion, extension and inflation of a cylindrical tube

Abstract

The non-homogeneous deformation of combined torsion, extension and inflation of a stress-softening cylindrical tube is discussed within the framework of a theory of isotropic stress-softening in incompressible isotropic materials. The theory is based on the idea that the stress-softening material is an inelastic material that remembers only the maximum previous deformation to which it has been subjected. This selective memory dependence is incorporated within general material response functions that are monotone decreasing functions of a stress-softening variable; the latter is a monotone increasing function of the maximum previous strain experienced by the material. Results demonstrating the effects of stress-softening are obtained for general stress-softening materials in combined torsion, extension and inflation. A special analytical model is used to illustrate some general results as well as to provide graphical examples. By deforming a cylinder successively, first in simple torsion and then in uniaxial extension, the concept of deformation-induced inhomogeneity is presented. Finally, it is shown that the overall effects of stress-softening in pure torsion are much smaller than the corresponding effects in uniaxial extension.